AP Calculus AB Chapters 6.3-6.5

What does the integral represent : area between the graoh of f(x) and x axis from x = a to x = b

Properties of the Definite Integral : (1) from a to a = 0 (2) from a to b with constant infront of equation can move to the beginning of integral (3) Addition or subtraction of equations within an integral equals two separate integrals added or subtracted(4) integral from a to b equals the integral from a to c plus the integral from c to b (see graph) (or can be integral from a to b equals the integral from c to a minus the integral from c to b

Rule when finding the derivative of an integral when upper limit is a function : HAVE TO USE CHAIN RULE

How to find a function (integral from a to x of f(t)dt) + C taht satisfies a certain derivative and has x and y values at a certain point : (1) Plug equation into integral using a different variable (2) Plug in x and y to their respective places in the equation (3) Make a = x so that the integral equals 0, find C